.Modelica_LinearSystems2.DiscreteTransferFunction.Analysis.timeResponse

Information

Syntax

(y, t, x) = DiscreteTransferFunction.Analysis.timeResponse(dtf, tSpan, responseType, x0)

Description

First, the discrete transfer function representation is transformed into a discrete state space representation which is given to DiscreteStateSpace.Analysis.timeResponse and the time response of the state space system is calculated. The type of the time response is defined by the input responseType, i.e.

Impulse "Impulse response",
Step "Step response",
Ramp "Ramp response",
Initial "Initial condition response"

The outputs y and x are calculated from the system equations of the discrete state space system for each time step t=k*dt.

Example

  DiscreteTransferFunction z = Modelica_LinearSystems2.DiscreteTransferFunction.z();
  Modelica_LinearSystems2.DiscreteTransferFunction dtf=(0.0023753*z^2 + 0.00475059*z + 0.0023753)/(z^2 - 1.89549*z + 0.904988);

  Real tSpan= 0.4;
  Modelica_LinearSystems2.Types.TimeResponse response=Modelica_LinearSystems2.Types.TimeResponse.Step;
  Real x0[1]={0,0};

  Real y[5,1,1];
  Real t[5];
  Real x[5,1,1]

algorithm
  dtf.Ts:=0.1;
  (y,t,x):=Modelica_LinearSystems2.DiscreteTransferFunction.Analysis.timeResponse(dtf,tSpan,response,x0);
//  y[:,1,1] = {0.00237529691211404, 0.0116282350020595, 0.0293927396867651, 0.0546913271597482, 0.0865678034508828}
//         t = {0, 0.1, 0.2, 0.3, 0.4}
//  x[:,1,1] = {0.0, 0.0, 1.0, 2.89548693586698, 5.58336953639396}

Interface

encapsulated function timeResponse
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.DiscreteStateSpace;
  import Modelica_LinearSystems2.DiscreteTransferFunction;
  import Modelica_LinearSystems2.Utilities.Types.TimeResponse;
  extends Modelica_LinearSystems2.Internal.timeResponseMask_tf_discrete;
  input TimeResponse response = TimeResponse.Step;
  input Real x0[DiscreteTransferFunction.Analysis.denominatorDegree(dtf)] = zeros(DiscreteTransferFunction.Analysis.denominatorDegree(dtf)) "Initial state vector";
end timeResponse;